A175548 -id:A175548 - cp's OEIS frontend

A336692 Binary weight of 1+sigma(n).

1, 1, 2, 1, 3, 3, 2, 1, 3, 3, 3, 4, 4, 3, 3, 1, 3, 2, 3, 4, 2, 3, 3, 5, 1, 4, 3, 4, 5, 3, 2, 1, 3, 5, 3, 4, 4, 5, 4, 5, 4, 3, 4, 4, 5, 3, 3, 6, 4, 5, 3, 4, 5, 5, 3, 5, 3, 5, 5, 4, 6, 3, 4, 1, 4, 3, 3, 7, 3, 3, 3, 3, 4, 5, 6, 4, 3, 4, 3, 6, 5, 7, 4, 4, 5, 3, 5, 5, 5, 6, 4, 4, 2, 3, 5, 7, 4, 4, 5, 5, 5, 5, 4, 5, 3

Offset: 1

Antti Karttunen, Jul 31 2020

nonn

Cf. A000120, A000203, A088580, A175548, A324294, A332459, A336691, A336693, A336694, A336695, A336696.

PARI
```
A336692(n) = hammingweight(1+sigma(n));
```

a(n) = A000120(1+A000203(n)) = A000120(A088580(n)) = A000120(A332459(n)).

A067342 Sum of decimal digits of sum of divisors of n.

Original entry on oeis.org

1, 3, 4, 7, 6, 3, 8, 6, 4, 9, 3, 10, 5, 6, 6, 4, 9, 12, 2, 6, 5, 9, 6, 6, 4, 6, 4, 11, 3, 9, 5, 9, 12, 9, 12, 10, 11, 6, 11, 9, 6, 15, 8, 12, 15, 9, 12, 7, 12, 12, 9, 17, 9, 3, 9, 3, 8, 9, 6, 15, 8, 15, 5, 10, 12, 9, 14, 9, 15, 9, 9, 15, 11, 6, 7, 5, 15, 15, 8, 15, 4, 9, 12, 8, 9, 6, 3, 9, 9, 9

Offset: 1

Labos Elemer, Jan 16 2002

			n=100, sigma(100)=217, SumDigit(217)=10, a(100)=10.

Antti Karttunen, Table of n, a(n) for n = 1..10000
Index entries for sequences related to sigma(n)

Cf. A000203, A007953, A077650, A175548.

Array[Total[IntegerDigits[DivisorSigma[1,#]]]&,90] (* Harvey P. Dale, Jan 02 2012 *)

vector(80, n, sumdigits(sigma(n))) \\ Michel Marcus, Apr 08 2015

a(n) = A007953(A000203(n)). - Michel Marcus, Dec 26 2013

Offset corrected to 1 by Michel Marcus, Dec 26 2013

A295660 Binary weight of Euler phi: a(n) = A000120(A000010(n)).

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 2, 2, 1, 1, 1, 2, 2, 1, 2, 2, 3, 1, 2, 2, 2, 2, 3, 1, 4, 1, 2, 1, 2, 2, 2, 2, 2, 1, 2, 2, 3, 2, 2, 3, 4, 1, 3, 2, 1, 2, 3, 2, 2, 2, 2, 3, 4, 1, 4, 4, 2, 1, 2, 2, 2, 1, 3, 2, 3, 2, 2, 2, 2, 2, 4, 2, 4, 1, 4, 2, 3, 2, 1, 3, 3, 2, 3, 2, 2, 3, 4, 4, 2, 1, 2, 3, 4, 2, 3, 1, 4, 2, 2

Offset: 1

Antti Karttunen, Nov 27 2017

nonn

Antti Karttunen, Table of n, a(n) for n = 1..65537
Index entries for sequences related to binary expansion of n

Cf. A000010, A000120, A175548, A293516.

Cf. A003401 (gives the positions of ones).

Array[DigitCount[EulerPhi@ #, 2, 1] &, 105] (* Michael De Vlieger, Nov 27 2017 *)

A295660(n) = hammingweight(eulerphi(n));

(define (A295660 n) (A000120 (A000010 n)))

a(n) = A000120(A000010(n)).

A337199 Binary weight of A337194(n) = 1+A000265(sigma(n)), where A000265(k) gives the odd part of k.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 3, 2, 1, 1, 1, 1, 1, 1, 2, 2, 2, 3, 1, 2, 1, 1, 1, 3, 2, 1, 1, 2, 1, 1, 1, 3, 1, 4, 2, 1, 1, 4, 3, 1, 2, 3, 2, 2, 1, 1, 4, 5, 2, 3, 3, 1, 2, 1, 2, 4, 1, 3, 1, 1, 3, 1, 3, 2, 2, 1, 1, 2, 2, 3, 3, 4, 1, 2, 1, 3, 2, 5, 5, 1, 3, 1, 3, 2, 1, 4, 4, 5, 1, 3, 1, 2, 1, 1, 3, 4, 2, 5, 3, 3, 3, 4, 1

Offset: 1

Antti Karttunen, Aug 20 2020

nonn

Antti Karttunen, Table of n, a(n) for n = 1..65537
Index entries for sequences related to sigma(n)

Cf. A000120, A000203, A000265, A161942, A336698, A337194.

Cf. also A175548, A336692, A337198.

A000265(n) = (n>>valuation(n,2));
A337199(n) = (hammingweight(1+A000265(sigma(n))));

a(n) = A000120(A337194(n)) = A000120(A336698(n)).

A318832 Restricted growth sequence transform of A278222(A000203(n)).

Original entry on oeis.org

1, 2, 1, 3, 2, 2, 1, 4, 5, 6, 2, 3, 3, 2, 2, 7, 6, 8, 6, 9, 1, 6, 2, 4, 7, 9, 6, 3, 4, 6, 1, 10, 2, 11, 2, 12, 5, 4, 3, 13, 9, 2, 5, 9, 8, 6, 2, 7, 8, 14, 6, 5, 11, 4, 6, 4, 6, 13, 4, 9, 7, 2, 5, 15, 9, 6, 6, 10, 2, 6, 6, 11, 9, 8, 7, 5, 2, 9, 6, 14, 16, 10, 9, 3, 11, 6, 4, 13, 13, 14, 3, 9, 1, 6, 4, 10, 5, 17, 8, 12, 11, 11, 5, 13, 2

Offset: 1

Antti Karttunen, Sep 04 2018

nonn

Sequence allots a distinct value for each distinct multiset formed from the lengths of 1-runs in the binary representation of A000203(n).

For all i, j: a(i) = a(j) => A175548(i) = A175548(j).

Antti Karttunen, Table of n, a(n) for n = 1..65537
Index entries for sequences related to sigma(n)

Cf. A000203, A278222.

Cf. also A286622, A304101, A318831.

up_to = 65537;
rgs_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), u=1); for(i=1, length(invec), if(mapisdefined(om,invec[i]), my(pp = mapget(om, invec[i])); outvec[i] = outvec[pp] , mapput(om,invec[i],i); outvec[i] = u; u++ )); outvec; };
A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t };
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
A278222(n) = A046523(A005940(1+n));
v318832 = rgs_transform(vector(up_to,n,A278222(sigma(n))));
A318832(n) = v318832[n];

cp's OEIS Frontend

A336692 Binary weight of 1+sigma(n).

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A067342 Sum of decimal digits of sum of divisors of n.

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A295660 Binary weight of Euler phi: a(n) = A000120(A000010(n)).

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A337199 Binary weight of A337194(n) = 1+A000265(sigma(n)), where A000265(k) gives the odd part of k.

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A318832 Restricted growth sequence transform of A278222(A000203(n)).

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